# LMIs in Control/pages/Stability of Lure systems

< LMIs in Control | pages

**The System**Edit

**The Data**Edit

The matrices .

**The LMI:** The Lure's System's StabilityEdit

The following feasibility problem should be solved as sufficient condition for the stability of the above Lur'e system.

**Implementation**Edit

**Conclusion**Edit

If the feasibility problem with LMI constraints has solution, then the Lure's system is stable.

**Remark**Edit

The LMI is only a sufficient condition for the existence of a Lur’e Lyapunov function that proves stability of Lur'e system . It is also necessary when there is only one nonlinearity, i.e., when .

## External LinksEdit

- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.